1. Field of the Invention
This invention relates to computational aeroelastic analyses. More specifically, the invention is a method for performing computational aeroelastic analyses using linear state-space models.
2. Description of the Related Art
When designing aerodynamic structures, it is important to understand if and under what aerodynamic conditions the structure will be stable and unstable. This is especially true if a structure is inherently flexible (e.g., a wing) such that unstable operation thereof leads to oscillations of the structure until failure occurs. Accordingly, the field of aeroelastics examines the interaction between a flexible structure and the unsteady aerodynamics generated by the structure. Since structure design generally includes performance predictions, it is necessary to predict the aeroelasticity of a particular design. To do this, computational aeroelastic methods are used to numerically simulate an aeroelastic process using computational techniques. In general, the computational techniques include the use of a mathematical model of the structure and an aerodynamic model of aerodynamic conditions of the structure.
Referring now to FIG. 1, traditional computational aeroelastic analyses use Computational Fluid Dynamics (CFD) codes that require the coupled feedback interaction of a linear structural model 10 and a nonlinear aerodynamic model 20 (i.e., the CFD code). This coupled feedback interaction consists of information 12 (e.g., structural modes such as displacements or deflections in the case of flexible structures) from structural model 10 being passed to nonlinear aerodynamic model 20. For a flexible aerodynamic structure such as a wing, information 12 from structural model 10 consists of the physical displacements of the structure due to an aerodynamic force. This physical displacement information is supplied to nonlinear aerodynamic model 20 in order to compute an aerodynamic response or force 22 induced by this structural displacement. The computed aerodynamic response 22 is then fed back to structural model 10 to compute new displacement information 12. This exchange of information repeats at each time step of a numerical solution and this coupled feedback interaction takes place wholly within the aeroelastic CFD code.
Nonlinear aerodynamic model 20 is significantly more complicated than linear structural model 10. Therefore, the computational efficiency of the coupled feedback interaction process is driven by the large computational expense of the nonlinear aerodynamic system defined by the CFD code. As a result, traditional computational aeroelastic analyses are very time-consuming and computationally expensive. The output from the repetitive feedback process described above are time histories of the response of the structure at a given flight condition. The output time histories indicate the level of stability (or instability) of the structure's configuration being analyzed at a given flight condition. Stability (instability) is determined by the convergence (divergence) of the time histories. By changing the flight condition and repeating this analysis as necessary, the region of the flight envelope where the configuration is safe (stable) or unsafe (unstable) is defined. Clearly, computation of the stability/instability boundary (i.e., also known as flutter) becomes very expensive and time-consuming since the above-mentioned process must be repeated at several conditions.
In addition, the output time histories are in a form that is not suitable for use by other structure-design disciplines such as controls or optimization. These disciplines have a very specific requirement for the types of mathematical models that can be analyzed. However, the output time histories from the traditional computational aeroelastic analyses are not in that form. Thus, the value of the information generated by traditional computational aeroelastic analyses is limited in that it cannot be readily utilized by other disciplines involved in the overall vehicle design process.